With a dedicated mission to the Martian moons, Phobos and Deimos, set to launch soon, there is a growing interest in further exploring these moons using low-thrust propulsion. This paper investigates the trajectory design for a sample-return mission from Deimos using fuel-free solar sail propulsion technology, aiming to maximize operational time near Deimos within a minimum permissible total mission duration. Time-optimal transfers between Earth and Deimos are sought by formulating and solving an optimal control problem using a direct pseudospectral method. Initial guesses for the direct method are generated by considering a patched circular restricted three-body problem (CR3BP) approximation and by searching for heteroclinic-like connections between the Sun-Earth and Mars-Deimos systems using the differential evolution algorithm. The obtained solution, with a maximum mission duration set to eight years based on the insights from initial guess generation, results in an optimal duration of stay at Deimos of 329 days with a mission duration of 7.7 years. Although the patched CR3BP approximation demonstrated valid transfer solutions for this study, it is deemed computationally inefficient for future trajectory designs for similar mission concepts targeting either only Phobos or both moons at once. Nevertheless, the trajectories obtained back and forth from Deimos are sufficiently optimal for a preliminary mission concept and validate the feasibility of achieving such a mission employing a solar sail.